$7.$ Use Figure $5\mathrm{.}3$ as a template, illustrate the operation of HoarePartition$($A$[1,6])$ on the array A Show all intermediate steps how the array is transformed.

$//$Partitions a subarray by Hoare$$s algorithm, using the first element

$//$ as a pivot

$//$Input: Subarray of array A$[0..$n $1],$ defined by its left and right

$//$ indices l and r $($l $$ r$)$

$//$Output: Partition of A$[$l$..$r$],$ with the split position returned as

$//$ this function$$s value p $$ A$[$l$]$ i $$ l; j $$ r $+1$

repeat

repeat i $$ i $+1$ until A$[$i$]>=$ p

repeat j $$ j $1$ until A$[$j p

swap$($A$[$i$],$ A$[$j $])$ until i $>=$ j swap$($A$[$i$],$ A$[$j $])//$undo last swap when i $>=$ j

swap$($A$[$l$],$ A$[$j $])$

return j$9$

$($a$)$